If two random variables x and y are independent, then d (ax+by) = d (ax)+d (by)+2abcov (x, y) = (a 2) d (x)+(b 2) d (y)+2abρ {√ d (x)} {
Extended data:
The variance of a random variable represents its dispersion and repeatability. The greater the variance, the worse the repeatability of random variables, that is, the lower the "reliability" of a single value.
On the other hand, the smaller the variance, the better the repeatability of random variables, which means the higher the "credibility" of a single value. At the extreme, if the variance is zero, it means that this random variable is simply a "constant", and getting a value is enough to represent all the values.
In experimental data processing (such as Genie 2000 software), each quantity (random variable) measured (calculated) generally gives the measured value and its uncertainty. This uncertainty is generally the standard variance of random variables. According to these two values, the value of the random variable can be estimated as follows, that is, it falls in the following interval with a certain probability (depending on w).